In this paper, we extend the Bayesian skill rating system of TrueSkill to accommodate
score-based match outcomes. TrueSkill has proven to be a very
effective algorithm for matchmaking --- the process of pairing
competitors based on similar skill-level --- in competitive online
gaming. However, for the case of two teams/players, TrueSkill only
learns from win, lose, or draw outcomes and cannot use additional
match outcome information such as scores. To address this deficiency,
we propose novel Bayesian graphical models based on the Gaussian and Poisson likelihood as extensions of TrueSkill
that (1) model player's offence and defence skills separately and (2)
model how these offence and defence skills interact to generate
score-based match outcomes. Furthermore, we show that our models can naturally integrate home field advantage in a principled way. We derive efficient Bayesian inference methods for inferring latent skills in the Gaussian models, and fast fixed-point iteration method for the variational inference in the Poisson model, which is more than 1000 times faster than a sampling-based method for the Poisson model. We evaluate the proposed models on three real data sets including Halo 2 XBox Live matches. Empirical evaluations demonstrate that the new score-based models (a) provide
more accurate win/loss/draw probability estimates than TrueSkill (in terms
of information gain), (b) provide competitive and often better win/loss/draw (multi-class) classification
accuracy, (c) provide reasonably accurate score predictions with an appropriate
likelihood --- prediction for which TrueSkill was not originally designed but
important in many real-world applications. Furthermore, the proposed variational Bayes method for learning and inference in the Poisson model is about 1000 times faster comparing with the sampling method and performs comparably. 